The Thai food giant CP Foods says it sells prawns to many leading supermarkets in the US, UK and across Europe.

The Guardian identified several of its customers and traced CP prawns to all of the top four global retailers – Walmart, Carrefour, Costco and Tesco – and other big-name supermarkets including Morrisons, the Co-operative, Aldi and Iceland.

We asked those named in our investigation to comment on our finding of slavery in their supply chains.

All said they condemned slavery and human trafficking for labour and conducted rigorous social audits. Some appeared already aware that slavery had been reported in the Thai fishing sector and said they were setting up programmes to try to tackle it.

Walmart, the world's largest retailer, said: "We are actively engaged in this issue and playing an important role in bringing together stakeholders to help eradicate human trafficking from Thailand's seafood export sector."

Carrefour said it conducts social audits of all suppliers, including the CP factory that supplies it with some prawns. It tightened up the process after alerts in 2012. It admitted that it did not check right to the end of its complex chains.

Costco told us it required its suppliers of Thai shrimp "to take corrective action to police their feedstock sources".

Tesco said: "We regard slavery as completely unacceptable. We are working with CP Foods to ensure the supply chain is slavery-free, and are also working in partnership with the International Labour Organisation and Ethical Trading Initiative to achieve broader change across the Thai fishing industry."

Morrisons said it would take the matter up with CP Foods urgently. "We are concerned by the findings of the investigation. Our ethical trading policy forbids the use of forced labour by suppliers and their suppliers."

The Co-operative was among those claiming it was already working to understand "working conditions beyond the processing level". "The serious issue of human trafficking on fishing boats is challenging to address and requires a partnership" in which it is actively engaged, it said.

Aldi UK said its contractual terms stipulate that suppliers do not engage in any form of forced labour. "Aldi will not tolerate workplace practices and conditions which violate basic human rights."

Iceland said it only sourced one line containing prawns from a CP Foods subsidiary but was pleased to note that CP was "at the forefront of efforts to raise standards in the Thai fishing industry".

The supermarket sector has been aware of conditions on some Thai fishing vessels for a while, thanks to reports from the UN and NGOs. In a 2009 survey by the UN inter-agency project on human trafficking (UNIAP) 59% of migrants who had been trafficked on to Thai fishing boats said they had seen the murder of a fellow worker.

Retailers have focused, however, on abuses that came to light further up the Thai prawn supply chain – in processing and packing factories or in companies subcontracted to peel prawns. It seems the parlous state of fish stocks and the pressure to monitor supply chains for sustainabilityhas made the issue of slavery visible. Two retailers who did not wish to be named said that when they started to look at where fish for prawn feed was coming from, it became clear that the boats engaged in illegal fishing were also likely to be using trafficked forced labour.

Retailers have joined an initiative called Project Issara (Project Freedom)to discuss their response and several were at a meeting with producers in Bangkok at the end of last monthat which slavery was discussed.